optical arrangement and an autostereoscopic display device incorporating the same

ABSTRACT

An autostereoscopic display lens arrangement comprises an array ( 9 ) of parallel lenticular lenses ( 11 ), wherein the lens array comprises first and second materials of different refractive indices ( 60,62 ) sandwiched between planar substrates, with the interface between the first and second materials defining the lens surfaces. The first material has a refractive index n 1 , the lens array has a lens pitch p and the lenticular lenses have a radius of curvature at their centre of R, and the lenses satisfy n 1  (p/2R)&gt;0.6. This arrangement gives reduced banding and loss of intensity at steep angles when used in an autostereoscopic display.

FIELD OF THE INVENTION

This invention relates to an optical arrangement for an autostereoscopicdisplay device and an autostereoscopic display device incorporating theoptical arrangement.

BACKGROUND OF THE INVENTION

A known autostereoscopic display device is illustrated in FIG. 1. Thisknown device 1 comprises a two dimensional liquid crystal display panel(LCD) 3 having a row and column array of display pixels 5 acting as aspatial light modulator to produce the display in the form of a staticimage or dynamic images such as for example video. For the sake ofclarity, only a small number of display pixels 5 are shown in FIG. 1. Inpractice, the display panel 3 might for example comprise about onethousand rows and several thousand columns of display pixels 5.

The structure of the liquid crystal display panel 3 is entirelyconventional. In particular, it comprises a pair of spaced transparentglass substrates, between which an aligned twisted nematic or otherliquid crystal material is provided. The substrates carry patterns oftransparent indium tin oxide (ITO) electrodes on their facing surfaces.Polarizing layers are also provided on the outer surfaces of thesubstrates.

Each display pixel 5 is associated with a switching element, such as athin film transistor (TFT) or thin film diode (TFD). The display pixelsare operated to produce the display by providing addressing signals tothe switching elements, and suitable addressing schemes will be known tothose skilled in the art.

The display panel 3 is illuminated by a light source 7 comprising, inthis case, a planar backlight extending over the area of the displaypixel array. Light from the light source 7 is directed through thedisplay panel 3, with the individual display pixels 5 being driven tomodulate the light and produce the display.

The display device 1 also comprises a lens arrangement in the form of alenticular sheet 9, arranged over the display side of the display panel3, which performs a view forming function. The lenticular sheet 9comprises an array of semi-cylindrical lenticular elements 11. Eachlenticular lens 11 has a longitudinal axis 10 and the lenses areextending such that their longitudinal axis are oriented parallel to oneanother. Only one lens 11 is shown in FIG. 1 with exaggerated dimensionsfor the sake of clarity. Thus, an array of elongate lenticular elements11 extending parallel to one another overlies the display pixel array,and the display pixels 5 are observed by a user or viewer through theselenticular elements 11. The lenticular elements 11 act as a light outputdirecting means to provide different images, or views, from the displaypanel 3 to the eyes of a user positioned in front of the display device1.

The above described device provides an effective autostereoscopic, orthree dimensional, display device if the produced display or imagecomprises multiple views. Such a display or image will, hereinafter, beindicated to be an autostereoscopic image having at least two sub-imageseach one of them representing a different view of the object to bedisplayed by the image. The at least two views are then displayed by thelens arrangement so that a viewer perceives a stereo, 3D or look aroundimpression of the object. In an arrangement in which, for example, eachlenticular element 11 is associated with two columns of display pixels5, the display pixels 5 in each column provide a vertical slice of arespective two dimensional sub-image. The lenticular sheet 9 directsthese two slices and corresponding slices from the display pixel columnsassociated with the other lenticular elements 11, to the left and righteyes of a user positioned in front of the sheet, so that the userobserves a single stereoscopic image.

In modifications of such a device, the lenticular lenses may be orientedwith their longitudinal axis slanted with a slant angle with respect tothe pixel column direction of the display panel or autostereoscopicimage. The modification provides advantages in terms of pixel resolutionloss sharing between horizontal and vertical display panel directions.As this is not the subject of the present invention, for a more detailedexplanation on the effects and mode of application reference is made toU.S. Pat. No. 6,064,424.

SUMMARY OF THE INVENTION

It is an object of the invention to provide an optical arrangement andan autostereoscopic display device incorporating such an opticalarrangement with improved performance.

This object is achieved with the optical arrangement, theautostereoscopic display device employing the optical arrangement andthe method of displaying an autostereoscopic image with the opticalarrangement as defined in the independent claims.

The dependent claims define advantageous embodiments.

The invention provides an optical arrangement that has, when it is inits lens mode, a lens arrangement with an array of lenticular lenseseach of which has a particular lens surface shape that, when tracingrays through the lenticular lens after they have entered one side of thelenticular lens, there exists at least one ray that hits the lenticularlens surface perpendicularly. Such an optical arrangement in its lensmode gives optimized optical effect in that when viewing an imagethrough it under large off normal viewing angles, image distortion isreduced. Hence, when applied to display autostereoscopic images, amarked improvement with respect to the so-called banding phenomenonand/or with respect to daylight cross-talk and/or dependency of theautostereoscopic effect upon the angle with which a viewer observes theautostereoscopic image on an autostereoscopic display device isobtained.

It was found by the inventors that a characteristic associated with theuse of cylindrical lenticular lenses, such as for example in the priorart device described in the preamble, is that, because of fieldcurvature, the intensity footprint changes with viewing angle. Theintensity footprint can be considered to be the size of an area ofillumination derived from a parallel beam with a width of one lens,which has passed through the lens at a given angle. The footprint sizeis measured at the display pixel plane. A narrow footprint means thelens is in focus at the display pixel plane, whereas a larger footprintmeans the lens is in focus at a different location, somewhere above orbelow the display pixel plane. A large footprint corresponds to angulardivergence of the views.

FIG. 2 is a graph illustrating the relationship between intensity (I) onthe y-axis (in arbitrary units a.u.) and position (P) at the pixel planeon the x-axis (millimeters) contributing to an image for viewing angles(VA) between 0° and 50° (annotations on the left of the FIG. 2). Thegraphs corresponds to a display having a lenticular lens that isoptically isotropic and for which there is a refractive index differenceat the lens surface of 0.5 between the refractive indices of the lensand air. In the FIG. 2 the positions on the x-axis of pixels whichcontribute to a particular view are displayed. It can be seen that thefootprint size is very large for viewing angles greater than 30°, wherea large physical width of pixels contribute to the view. Note that thedotted lines are the results after being convoluted with a top-hatdistribution taking into account the effect of pixel size and the slantangle with which the lenticulars are slanted with respect to the columndirection of pixels. A large footprint size is undesirable since itcauses excessive overlap between views, generating excessive crosstalkbetween views and therefore reduces the 3D impression.

In addition to the broadening of views shown above for large viewingangles, a banding effect, which is often referred to as a Moiré-type ofartefact, can also arise for smaller viewing angles. This is caused bythe fact that the focus of the lenticular lenses shifts towards theviewer with increasing, off-normal, viewing angle.

The lens arrangement of the optical arrangement of the present inventionreduces and/or mitigates these and other effects.

In the claims, the terms ‘first and second layer’ are not to beconstrued as necessarily meaning to refer to continuous layers. Thus,for example the first layer may be composed of multiple volumes with afirst refractive index embedded in the second layer having the secondrefractive index. This is further explained with reference to thedescription concerning switchable optical arrangements according to theinvention.

The desired advantageous effects of the invention increase withincreasing magnitude of the product defined in claim 1. Thus, forexample, the viewing angle under which an autostereoscopic imagedisplayed by that device may be observed with improved quality increaseswith increasing the product defined in claim 1. Thus, preferably thelens arrangement is designed such that the product is greater than 0.6,0.7, 0.8, 0.9, 1.0, or even 1.1. Preferably the product is greater than0.8, this provides a balance between the effect obtained and themanufacturability of the optical arrangement with respect to materialsneeded.

The desired effect is dependent on the lens pitch within the array oflenticular lenses. The lens pitch is to be construed as the width of alenticular lens measured in a direction of curvature. The lens pitch isthus measured perpendicularly to for example the longitudinal axis ofthe lenticular lens 11. The radius of curvature at the centre of thelens is the radius of curvature as measured in the middle of thelenticular lens or halfway a lens pitch within a section of thelenticular lens taken perpendicular to the longitudinal axis 10.

The lens pitch may be bound by a minimum value determined by theautostereoscopic image to be displayed. For example, the lower boundaryof the lens pitch may be determined by the resolution or number of viewsof an autostereoscopic image and thus the number and dimensions ofdisplay panel pixels that is associated with one lenticular lens in adisplay device. When using the minimum applicable lens pitch the productas defined in claim 1 may be adjusted by designing the lens withappropriate radius of curvature or first index of refraction.

The desired advantageous effect may be dependent on the orientation ofthe lens with respect to an autostereoscopic image to be projected byit, or observed through it.

This dependency will be larger when the refractive index differencebetween the first refractive index and the second refractive index islarger. One can define the optical arrangement and therewith the lensarrangement to have a viewer side and a display side. The opticalarrangement preferably has the first layer as its viewer side as thenthe advantageous effect obtained is largest.

In an embodiment of the lens arrangement, the first refractive index isthe lowest refractive index of the first and second refractive indices.This has the advantage that the desired effect based on the designcriteria defined in claim 1 for the particular design is achievedindependent of orientation of the lens arrangement with respect to anautostereoscopic image to be displayed.

The difference between the refractive indices of the respectivematerials, Δn, is preferably smaller than in conventional lenses, inparticular in the range 0.05-0.22. This not only reduces the dependencyon orientation explained here above and therewith creates freedom ofuse, but also provides a lens arrangement with less reflectance,enabling the observing of images with fewer disturbances caused by thesereflections. Other possible refractive index difference ranges are0.05-0.15 and 0.09-0.12. The difference may be 0.1.

The highest refractive index of the first and second refractive indicesmay be in the range 1.4 to 1.65. This may be achieved for example byproviding the relevant first or second layer such that it comprises anacrylic material or polycarbonate. A high refractive index isparticularly advantageous for the desired effect if the high refractiveindex is the first refractive index, as then a higher radius ofcurvature may be used, translating to less curved lenses that are moreeasy to manufacture than more curved lenses.

The layer having the lowest refractive index may have a refractive indexin the range 1.3 to 1.5, for example by providing that that the layerhaving this refractive index comprises a silicone material. The firstand second materials may have substantially the same Abbe number.

The first and second layers may be made of all solid material, so thatno support layers or substrate layers are needed. Alternatively, one ofthe layers, e.g. the first layer, may be a solid layer while the otherlayer, e.g. the second layer is a liquid or gas. The one solid layerthen may have the shape of the lenticular lens surface requiredaccording to the definition of claim 1. In these cases support layersmay be added to the optical arrangement such that the lens arrangementis sandwiched between the support layers.

The first and second substrates preferably comprise planar glass orpolymer material such as for example polycarbonate or other transparentmaterials.

The first layer may comprise a lens layer which defines convexlenticular lens shapes, and has a higher refractive index than thesecond material, which comprises a replica layer and fills the spacingbetween the convex lenticular lenses.

The optical arrangement may be a switchable arrangement that can switchbetween the lens mode and a further mode of operation. The further modemay for example have no substantial lens effect. Such an opticalarrangement with a further mode without lens effect would enableautostereoscopic viewing with the advantages of the lens mode and twodimensional viewing in the further mode with the advantages of highresolution ideal for e.g. text display. The switchable arrangement maycomprise one or more electrodes and an electro-optic material or layersuch as a liquid crystal material in combination with one or morepolarisers.

According to the invention there is provided an autostereoscopic displaydevice comprising an image providing means and the optical arrangementpositioned in front of the image providing means. The image providingmeans preferably comprises an array of image pixels or display pixelsbeing arranged in rows and columns, for defining an autostereoscopicimage. The optical arrangement is arranged so that in the lens mode ofthe optical arrangement the direction of outputs of groups of the imageor display pixels are projected in respective different directions as aplurality of views. The image providing means may be a means forproviding a static image in any kind of form, such as for example anautostereoscopic postcard or photo. Alternatively, the image providingmeans may be an electronic display means providing static and/or dynamicautostereoscopic images. Such an electronic display means includes butis not limited to a liquid crystal display, a plasma display, cathoderay tube display or light emitting diode based display. Theautostereoscopic display benefits from the advantageous as explainedhere before. Especially a display wherein the optical arrangement ispositioned such that when in the lens mode, the first layer is on theviewer side of the optical arrangement is advantageous for the obtainedadvantage as described here above.

The optical arrangement may be mechanically attachable and/or detachablefrom the image display means.

According to the invention there is provided a method of displaying anautostereoscopic image, comprising providing an autostereoscopic imageand projecting the autostereoscopic image through a lens arrangementaccording to the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, purely by way ofexample, with reference to the accompanying drawings, in which:

FIG. 1 is a schematic perspective view of a known autostereoscopicdisplay device;

FIG. 2 is a graph illustrating an exemplary relationship betweenintensity and position at the pixel plane contributing to an imageproduced by the device of FIG. 1 for viewing angles between 0° and 50°;

FIG. 3 is a schematic cross-sectional view of a known autostereoscopicdisplay device;

FIG. 4 shows graphs to illustrate in more detail the view overlap, viewbroadening and loss of intensity at large viewing angles which can arisewith the known lens structure of FIG. 4;

FIG. 5 is a schematic cross-sectional view of an example of anautostereoscopic display device according to an embodiment of theinvention;

FIG. 6 shows the reduction in view broadening and improvement inintensity at large viewing angles which is achieved by the lensarrangement of the invention;

FIG. 7 shows the reduction in view overlap which is achieved by the lensarrangement of the invention;

FIG. 8 shows how the performance of a lens in accordance with theinvention differs from a conventional lens;

FIG. 9 shows an expanded view of FIG. 8;

FIG. 10 shows how the lens function can be considered as a functionwhich probes the pixel structure;

FIG. 11 shows the beam intensity distribution function;

FIG. 12 shows the decay of the power of the beam profile spectrum atdifferent cross-sections;

FIG. 13 is used to explain the difference between the lens of theinvention and the conventional lens in respect of the sharpness acrossranges of input angles;

FIG. 14 shows the plot of maximum sharpness for the lens of theinvention;

FIG. 15 shows schematically how the lens of the invention providesimproved sharpness;

FIG. 16 is used to show the various lens geometrical parameters;

FIG. 17 is used to show the region for which perpendicular lightincidence is ensured and

FIG. 18 is a schematic cross-sectional view of an example of anautostereoscopic display device according to an embodiment of theinvention.

The dimensions of the diagrams are not to scale and like referencenumerals refer to like elements throughout the text.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 3 shows a schematic view of a typical known autostereoscopic or 3Ddisplay device 30. It consists of a display panel in the form of aliquid crystal display (LCD) display 31, with a glass spacer plate 32.The 3D display device has as its optical arrangement a lens arrangement33 for example comprising acrylic lenses 35 over a glass substrate 34.The FIG. 3 shows a cross sectional view of the display of FIG. 1perpendicular to the longitudinal axis of the lenticular lenses. Threelenses 35 are shown having a width equal to the lens pitch array p. Inthis design, the refractive index difference at the lens boundary, i.e.the surface of the lenses 35 at their side opposite to the glasssubstrate 34, is approximately 0.5, as the interface is between the lenslayer having, for example, a refractive index of 1.5 and air.

In this particular case 9 display pixels are associated with everylenticular lens 35, meaning that each lens overlays a group 36 of 9pixels and therewith in principle could create 9 views as each pixelimage is sent to a different direction one overlying lens.

FIG. 4A shows the light intensity (I) as a function of the viewing angle(VA) for a 42 inch (107 cm) product according to the geometry of FIG. 3.The lower set of curves show the individual views 41, which for reasonsof clarity have not all been indicated with the reference numeral. Thetotal intensity integrated over all views is shown in the upper curve42.

For increasing angles beyond 0.4 radians, the width of the views 41, forexample measured as full width at half maximum, increases significantly,and this is also accompanied by a drop in intensity I. The drop inintensity is especially evident from views 41 at viewing angles beyond0.5 radians. The drop in intensity is also found from the upper curve 42which bends downwards in the graph of FIG. 4A. The view width can beseen to increase because the sides of the curves become less steep. Asan illustration, FIG. 4B shows the overlap (O) between neighboring views41 as a function of the viewing angle (VA). The overlap (O) is definedin FIG. 4C. By definition, two completely separated views have zerooverlap and identical views have an overlap that equals one. In FIG. 4B,a relatively steep increase in the overlap occurs for angles exceeding0.4 radians. The larger the overlap, the more crosstalk between views.

It is further observed from the upper curve 42, that intensityvariations occur especially for viewing angles in the ranges 43, i.e.approximately between a viewing angles of −0.1. to −0.6 or 0.1 to 0.6radians. These variations are perceived by the viewer as the bandingpreviously mentioned.

The invention provides an optical arrangement having in its lens mode alens array consisting of the corrugated interface of two differentmaterials. The lens geometry and material composition is designed in away which optimizes the lens performance, as explained further below, toobtain the advantage effect of the invention.

FIG. 5 shows an embodiment of an autostereoscopic display device 50according to the invention. The device has an image forming means in theform of a display panel 51 with a glass plate 52. The autostereoscopicdisplay device has an optical arrangement 53 according to the inventionon top of the image forming means. In this particular case thearrangement is not switchable and is in its lens mode permanently. Theembodiment comprises an array of semi cylindrical lenticular lenses 55that are oriented parallel with their longitudinal axes. The lens arraycomprises first 55A and second layers 55B sandwiched between planarglass substrates 54, 57. The interface between the first 55A and secondlayer 55B defines the corrugated lens surface 58. In this particularcase the first and second layers are optically isotropic and have arefractive index difference between 0.05 and 0.22 for radiation withinthe visible light spectrum.

The first layer 55A comprises a lens layer which defines convexlenticular lens shapes. In the present embodiment this layer comprises amaterial, with a refractive index of around 1.5, for example an acrylicmaterial including: 80% Ethoxylated bisphenol A diacrylate (SR-349 from“Sartomer Company, Inc”) and 20% trimethylolpropane triacrylate (TMPTA)with a refractive index of around 1.53. The second layer 56 is made of asilicone rubber material (Elastosil RT604 from “Wacker chemicals Inc”)and has a refractive index of around 1.41.

Although the example is described with the aforementioned combination offirst and second layers, combinations of other layers can be equallywell applied within the general concept of the invention. Thus forexample, the refractive index of the first layer may be in between 1.4and 1.6 so that polycarbonate with a refractive index of around 1.59 maybe used together with the silicone rubber material. Yet still othermaterials with appropriate refractive indices may be used without lossof effect of the invention.

Also, the invention is not restricted to these ranges of refractiveindices or the ranges of refractive index difference to the materialsdefined here above. The materials mentioned can be replaced by any othermaterials with the appropriate refractive index chosen such that therequired difference of refractive index is obtained in relation to theradius of curvature and lens pitch desired for the lens surfaceaccording to the invention. Various modifications will be apparent tothose skilled in the art.

The acrylic material lens structure of the present embodiment can bemade by a replication process. In such a process a mould is providedhaving a relief surface that is complementary to the shape of the lens,i.e. for example the layer 55A. In a replication step, the layermaterial is brought in contact with the mould such that it takes therelief shape of the mould and is fixed in that shape. The resulting lenscan be attached to a substrate layer 57 for example for providingstrength during molding or afterwards. The substrate can be removed ifit was just to sustain the lens structure during the replicationprocess. The replicated lens, with or possibly without the substratelayer is then embedded into a silicone layer that is supported by asupport layer such as for example a glass plate or plastic plate. Theacrylic material mentioned here before may be conveniently used in sucha process. However, any other material that can be molded in such a waymay be used as long as the final result is a layer with the appropriaterefractive index when compared to that of the other layer.Alternatively, the silicone layer is applied to the replicated lensfollowed by application of the support layer. Any one of the substratelayer or the support layer may be made for example of glass. Glass hasamongst others the advantage of having a flat surface and is commonlyused within display industry. It will be evident that the substratelayer and/or support layer must be able to withstand possible conditionsduring the manufacturing steps so that the resulting structure isprevented from unwanted distortions and the like.

Alternatively, the lens structure may be mechanically machined. Ingeneral this requires lens materials that are solid at the machiningconditions (temp and pressure) For example a polycarbonate lens may bemade advantageously in this way.

In the embodiment of FIG. 5 the lens arrangement 53 has beenincorporated in an autostereoscopic display device 50 according to theinvention. Thereto the lens arrangement is attached to a display panelin the form of a (LCD) 31 having a glass spacer plate 32.

FIG. 6 shows the light intensity (I) as a function of the viewing angle(VA) for a 42 inch (107 cm) product according to the geometry of FIG. 5.As in FIG. 4, the lower set of curves 61 (not all annotated withreference numerals) show the individual views. The total intensity isshown in the upper curve 62.

A typical lens radius for the structure of FIG. 3 is 2.212 millimeter,but in FIG. 6, the lens radius (R) is only 0.519 millimeter. This isbecause the focal distance is approximately equal to the quotient oflens radius (R) and refractive index difference of the layers definingthe lens surface and the focal distance parameter is thus keptapproximately constant for the lens structure of the invention to beused in the same application as the known lens structure of FIG. 3. Theprecise desired radius can be determined to minimize the bandingintensity, and this is explained below. The reduced lens radius givesrise to deeper lenses if the lens is to cover the same area, i.e. coverthe same number of columns of pixels of a display means. In this casethat would be 9 pixels in the groups 36 or 56 of FIGS. 3 and 5,respectively.

FIG. 6 shows that, apart from a low intensity tail, the broadening ofthe views is much less for the design of the invention. Moreover, thebanding has reduced significantly. This is partly due to the somewhatsmaller field curvature of the lens. For a similar geometry, with theacrylic part of the lens oriented towards the viewer, a similar behavioris observed, but with the low intensity tail of the views oriented awayfrom the origin.

FIG. 7 shows the overlap as a function of viewing angle for comparisonwith FIG. 4B. For the lens design of the invention, the overlap-curve isvery flat. The design gives a marked improvement in the viewingexperience under larger off-normal viewing angles (VA).

In addition to the reduction in cross-talk and banding, the design ofFIG. 5 has the additional advantage of a low reflectivity. The upperflat surface of the upper glass plate can be easily coated with ananti-reflection coating. Due to the low refractive index difference, thelens structure itself has low reflection. Another advantage is that theouter surface of the device is flat and robust. There is no need for anadditional protective plate in front of the display as one of the lensarrangement substrates can provide this function.

The lens design of the invention thus provides a reduction in angulardependent cross-talk, a reduction in banding, low reflectivity and adesign which can be arranged with robust flat sides having advantagesfor several reasons mentioned here above.

Although in the examples given above, the first and second layers aresandwiched between substrate layers, this is not mandatory. In anembodiment, the first layer 55A and the substrate layer 57 are one andthe same layer. Accordingly, the second layer 55B and the substratelayer 54 may be one and the same layer. This may especially be so whenthe first and second layers are strong enough so that no substratelayers are necessary.

In an alternative embodiment of an autostereoscopic display deviceaccording to the invention, the layer 52, which is part of the displaypanel in the embodiments given here above, may form the substrate layerof the lens arrangement, thus combining the function of these layerswith the opportunity to reduce cost weight or manufacturing time.

As mentioned above, the lens array is designed not only based on therefractive index difference, but also based on the geometry of the lens,in particular the lens radius R and lens pitch p.

FIG. 8 schematically shows how the performance of a lens 80 with highrefractive index difference and therefore small curvature (top part ofFIG. 8, differs from a lens with low refractive index difference andtherefore large curvature (bottom part of FIG. 8. The top part of FIG. 8shows a lens with refractive index difference 0.5 with air at one of theinterfaces, and lens radius of 0.333 times the focal length. The bottompart of FIG. 8 shows a lens with refractive index difference 0.1 andlens radius of 0.067 times the focal length.

Light is entering the lens 80 coming from the left. The high refractiveindex air lens provides a well shaped beam with well defined focus 81.The low refractive index difference lens has larger curvature andtherefore more spherical aberrations. The beam behind the lens shows socalled “caustics” in region 82. In this region, the rays catch up ontoeach other, giving a local high intensity. The focal distance f is thedistance behind the lens at which rays close to the axis intersect.

FIG. 9 shows an expanded view of the lower example from FIG. 8. Theintensity distribution at several positions along the beam is shown. Inthe region 80 where the caustics occur the beams show two loci withintensity maximas (see plot 90). At the tip of the caustics (plot 92)the two loci coincide to form one point of high intensity. To the rightof this point the intensity distribution becomes smooth again. Plot 90can be considered to be a “caustic edge” of the lens, and plot 92 is the“caustic tip”.

The invention is based on the understanding of how this opticalperformance, which suffers from worse optical aberrations, can give riseto the improved angular performance as explained above. In order tounderstand how the lens design influences the performance of the opticalsystem, the lens function can be considered as a function which probesthe pixel structure. This is explained schematically in FIG. 10. Theleft part shows a beam profile 100, created by the lens that is notshown, modulating light associated with the pixels of the pixel array110. This is a low pass filter convolution function as shown in theright of FIG. 10.

The convolution function results in a loss of information entropy (seefor a more detailed explanation of the term Information Entropy forexample C. E. Shannon in A Mathematical Theory of communication, TheBell System Technical Journal, Vol. 27 pp. 379-423, 623-656 July,October, 1948).

FIG. 11A shows the beam intensity distribution function 100 as a valueI(y) where y is the displacement from the central axis.

The entropy loss is based on the Fourier transform of the function 100:

Y(k)=

(I(y))

The entropy loss is defined as:

${\Delta \; H} = {{- \frac{1}{W}}{\int_{W}^{\;}{{\log \left( {{Y(k)}}^{2} \right)}{k}}}}$

FIG. 11B shows the log value used to derive the entropy loss.

A beam profile with the slowest decaying log function (i.e. the slowestdecaying power spectrum) will have the least information loss (thesmallest area between the curve of FIG. 11 and the x-axis), andtherefore contain the most high frequencies. This can be considered torepresent a “sharpness” function.

FIG. 12 on the right shows the decay of the power spectrum of the beamprofile spectrum at different cross-sections. Clearly, the profile atthe caustic tip has the slowest decaying power spectrum. If the caustictip is not present, which is the case at sufficiently large angles ofincidence of the bema on the lens, then the profile at the caustic edgehas the next best beam profile spectrum.

The analysis above enables a maximum sharpness point to be defined, asthe point where the power spectrum of the profile decays most slowly.There is a clear difference between the low refractive index differencelens and the conventional lens, as shown in FIG. 13.

Plot 130 is the position of the focus defined as the intersection of theadjacent rays that impinge upon the lens surface close to the center ofthe lens (i.e. the crossing of the lens surface and the optical axis).Plot 132 is the position of the point where the Root Mean Square (RMS)width of the beam is smallest. Differently stated, the point where thecross section of the beam is smallest. The significant difference is themaximum sharpness point shown by plot 134. For the low-Δn lens, thiscurve has a much larger radius of curvature when compared to the normallens. This means that for larger angles of incidence, the maximumsharpness point remains comparatively much closer to the original focalplane. In fact, the curve for the low-Δn lens is made up by the caustictip point rotating around the centre of the lens (in this case centremeans the centre of the sphere which forms the lens). For the normallens, the curve for larger angles is made up by a point on the causticedge region (the tip is missing).

Thus, it can be seen that if the lens can be designed to provide acaustic tip region which covers all angles of incidence, then thesharpness can be improved. FIG. 14 shows the plot of maximum sharpnessand shows the caustic tip region 140 and caustic edge region 142. Thecaustic tip is present if one of the incoming rays hits the lens surfaceperpendicularly. This ray goes through the centre of the sphere definingthe lens surface. If the angle of incidence of the rays is too large(for a given aperture of the lens), the tip is no longer present.

This enables a set of design parameters for the lens to be determined.As shown in FIG. 15, Incoming rays are bent towards the normal,confining the angular range within the first layer of an opticalarrangement. The lens can be designed with Δn sufficiently small, i.e.the lens is sufficiently curved, such that for every incoming angle(corresponding to the full angular range in air) at least one ray hitsthe lens surface perpendicularly. This design rule then provides aregion of greatest sharpness close the pixel plane, and thereby providesthe advantages outlined above.

The pixel plane of the display is in the vicinity of the vertical line150, and the viewer is at the left. For simplicity, FIG. 15 shows raysbeing directed from the viewer towards the display but the analysis doesnot change when considering light directed through the display pixels tothe viewer.

There are a number of ways to characterize the lens design to providethis continuous caustic tip, which in turn gives rise to the improvedsharpness explained above.

FIG. 16 is used to show the various lens geometrical parameters.

The number of views is determined by the lens pitch p. The range ofviewing angles, defined by the primary cone angle γ, is determined bythe lens pitch p, the distance d from the pixel plane 40 to the lens,and the refractive index n2.

Given p, d, n1 and n2, the lens radius R is optimized for minimumbanding. This lens radius R determines the focal length f, which isslightly larger than the distance d in the example shown. It is known tooffset the pixel array from the focal distance, in order to reduce theeffect of imaging of the black mask layer of the LCD panel.

In addition to the low refractive index difference discussed above, theoptical performance of the lens can be characterized by a parametern1(p/2R), where the values of n1, p and R are all shown and explainedwith reference to FIG. 16. This dimensionless parameter takes intoaccount the lens curvature as well as the focal distance, and thebending of light as it enters the lens body. In particular, with n1defined as the part of the lens arrangement on the viewer side, thistakes into account the bending at the air interface on the viewer side.This parameter enables the requirement for light to be incidentperpendicularly to the lens surface to be satisfied.

FIG. 17 shows the region for which perpendicular incidence is ensured asthe shaded region. The sloping left boundary of the shaded area isdetermined by:

For n1>√2

n1(p/2R)=1

For n1≦=√2

n1(p/2R)=n1²/2√(n1² −1)

The right vertical boundary is given by:

p/2R=1.

For a circular lens, the pitch cannot exceed two times the radius, andthis dictates the right boundary.

The boundary of the area in FIG. 17 is based on n1(p/2R)=1 and pointswithin the boundary satisfy n1(p/2R)>1.

The invention applies more generally to values of n1(p/2R)>0.6. Morepreferably, n1(p/2R)>0.8. Even more preferably, n1(p/2R)>1.

In FIG. 17, region 180 represents feasible lens geometries, and region182 represents currently most readily available materials for the lensbody (excluding n1=1). This gives a region 184 which is based oncurrently available materials and which satisfies the most preferredlens design parameter range of the invention.

The examples of FIGS. 8 to 17 have n1<n2 with the outwardly curved lensfaces pointing to the viewer. The same relation holds for the geometrywhere the lenses are pointing in the reverse direction, for example asshown in FIG. 5. In this case, the outwardly curved lens faces pointtowards the display panel, and n1>n2 to create a positive lens.

The invention is applicable to all types of positive lenses and has itsadvantageous effect in all types of lenticular lens basedautostereoscopic displays. Thus, the refractive index difference betweenthe layers forming the lens interface need not be small, as long as therelation of the refractive index, the lens pitch and the lens surfacecurvature according to the invention is fulfilled, as then theadvantageous effect is obtained.

In practice the lens system may consist of more than two or three media,e.g. intermediate glass plates/layers or air gaps.

The discussion and analysis above is based on spherical lenses. However,aspherical lenses may be used (for example having two effective radii).The analysis above can then be considered to be based on the effectivelens radius at the centre of the lens (along the central optical axis).

The refractive index of a material depends on the wavelength of thelight. This is usually expressed in terms of the so called “Abbenumber”. Due to the wavelength dependence, the focus of the lens dependson the color of the light. When making a lens of two materials with onlya small difference in refractive index, the color dependency of the lensas a whole will scale up with roughly a factor of(n_(acrylic)−n_(air))/(n_(acrylic)−n_(silicone))≈5, resulting in colordependent banding. To avoid this, the Abbe numbers of the differentmaterials should be matched.

The Abbe number is defined as:

$V = \frac{n_{D} - 1}{n_{F} - n_{C}}$

wherein n_(D), n_(F), n_(C) are refractive indices of the material atthe D- F- and C- spectral lines (589.2 nm, 486.1 nm, 656.3 nmrespectively).

The refractive index differences mentioned above “in the visiblespectrum” may be assumed to be measured at a single point within thevisible spectrum, for example the D₃ helium line at 587.5618 nm.

The lenticular lenses are preferably slanted with respect to the columnsof pixels of the display, and this is a known measure to share the lossof resolution resulting from the lens array between the row and columndirections of the display.

The design of liquid crystal display has not been explained in detail,or the image processing required to generate the required multipleviews. These are all standard, and the invention provides a change onlyto the lens design.

In the example above, the lens layer 60 is an acrylic material, but itmay instead be a polycarbonate material (refractive index n=1.59−1.60),and this could be combined with a silicone material as the secondmaterial layer 62.

In an embodiment as represented by FIGS. 18A and 18B, the opticalarrangement may have an area 200 as represented by FIG. 18B wherein theinterface between the layers defining the lens surface is substantiallyflat. This nonlens area may then be used to display for example 2D dataof any kind. The nonlens area (200) then has the same refractive indexdifference as the lens area FIG. 18A with the advantage that theboundary between the two areas will be masked, i.e. will be less visiblefor a viewer compared to a situation where a nonlens area is notprovided with the layered structure of the lens area having the lowrefractive index differences. Hence a display appearance is improved. Itwill be clear that multiple of such areas may be provided as well asthat multiple lens areas may be provided according to need. Such may beimportant for display systems that must provide 3D data and 2D data atthe same time. This arrangement and corresponding display having annon-lens area with the two layers with low refractive index may also beused independently from the requirement of lens radius as defined by thefeature ‘wherein the product of the first refractive index with the lenspitch divided by two times the radius of curvature is greater than 0.6’in the current invention without loss of the described advantage.

The invention can be used in displays generally, and this includeselectronic photo frames and other display output devices.

Various modifications will be apparent to those skilled in the art.

Preferably, the surfaces of the first and second layers opposite tothose forming the lens surface are both planar. While one of thesesurfaces allows easy mounting of the lens arrangement on a planarsurface of a display device such as a regular liquid crystal display(LCD), the other may be provided with additional layers such as forexample antireflection coatings, and/or other optical layers, and/oranti-scratch and/or other protection coatings. Hence, the additionallayers are advantageously not situated between the lens arrangement andthe surface of the display panel, thereby not disturbing the opticaleffect or optical output of the autostereoscopic display device achievedwith the lens arrangement.

The present invention is applicable to all optical arrangements with alens function, especially when used for autostereoscopic display. Thus,the optical arrangement may be a switchable arrangement having the lensfunction according to the invention in one mode and another opticalfunction in a further mode. An optical arrangement that is switchablemay for example be constructed as described in WO1998/021620A1. Theoptical arrangement then comprises an electrode structure and a liquidcrystal (LC) material to function as one of the first or second layer ofthe optical arrangement. The refractive index of the liquid crystallayer is anisotropic and dependent on the orientation of the liquidcrystal molecules. The electrode structures serve to provide electricalfields across the layer in order to align the LC molecules in one of themodes of the optical arrangement. Thus, in the lens mode the LCmolecules are oriented such that there is a refractive index differencebetween the first and second layers, while in the further mode thisrefractive index difference may be substantially absent due toappropriate reorientation of the LC molecules thereby benefiting from adifferent refractive index of the LC layer.

Other principles of providing switchable lens arrangements may be usedto prepare an optical arrangement according to the invention. Thus forexample fluid focus lenses may be used.

In the claims, any reference signs placed between parentheses shall notbe construed as limiting the claim. The word “comprising” does notexclude the presence of elements or steps other than those listed in aclaim. The word “a” or “an” preceding an element does not exclude thepresence of a plurality of such elements. In the device claimenumerating several means, several of these means may be embodied by oneand the same item of hardware. The mere fact that certain measures arerecited in mutually different dependent claims does not indicate thatthe combination of these measures cannot be used to advantage.

1. An optical arrangement having at least a lens mode in which it is alens arrangement comprising an array (9) of positive lenticular lenses(11), each respective one of the positive lenses comprising a firstlayer and second layer having an interface between each other definingthe lenticular lens surface, the first layer having a first refractiveindex and the second layer having a second refractive index that isdifferent from the first refractive index, the lens array having a lenspitch and the lenticular lens surfaces having a radius of curvature attheir centre, wherein the product of the first refractive index with thelens pitch divided by two times the radius of curvature is greater than0.6.
 2. An optical arrangement as claimed in claim 1, wherein theproduct is greater than 0.8.
 3. An optical arrangement as claimed inclaim 1, wherein the product is greater than
 1. 4. An opticalarrangement as claimed in claim 1, wherein the lens arrangement has aviewer side opposite to a display side and the first layer is on theviewer side of the lens arrangement.
 5. A lens arrangement as claimed inclaim 1, wherein the first refractive index is the lowest refractiveindex of the first and second refractive indices.
 6. A lens arrangementas claimed in claim 1 wherein the absolute value of the refractive indexdifference between the first and second refractive indices is in between0.05 and 0.22.
 7. A lens arrangement as claimed in claim 6, wherein theabsolute value is between 0.05 and 0.15.
 8. A lens arrangement asclaimed in claim 1 wherein the highest refractive index of the first andsecond refractive indices is in the range 1.4 to 1.65.
 9. A lensarrangement as claimed in claim 1, wherein the lowest refractive indexof the first and second refractive indices is in the range 1.3 to 1.5.10. A lens arrangement as claimed in claim 1 wherein the first layer andthe second layer are optically isotropic.
 11. A lens arrangement asclaimed in claim 1, wherein the first and second layers havesubstantially the same Abbe number.
 12. A lens arrangement as claimed inclaim 1 having an area wherein the interface between the first layer andthe second layer is substantially flat.
 13. An autostereoscopic displaydevice comprising: an image providing means (3) and an opticalarrangement (9) according to claim 1 positioned in front of the imageproviding means.
 14. An autostereoscopic display device according toclaim 13, wherein the image forming means is an electronic display panel(3)
 15. An autostereoscopic display device according to claim 13,wherein the optical arrangement is positioned such that when in the lensmode, the first layer is on the viewer side of the optical arrangement.16. An autostereoscopic device according to claim 13 wherein the lensarrangement is positioned such that the second layer is closer to theimage providing means than the first layer and wherein the secondrefractive index is the lowest refractive index of the first and thesecond refractive indices.
 17. A method of displaying anautostereoscopic image, comprising providing an image comprisingmultiple views and projecting the image through a lens arrangementaccording to claim 1.